Foundations of Physics 40 (11):1744-1778 (2010)

Abstract
The goal of this paper is to introduce the notion of a four-dimensional time in classical mechanics and in quantum mechanics as a natural concept related with the angular momentum. The four-dimensional time is a consequence of the geometrical relation in the particle in a given plane defined by the angular momentum. A quaternion is the mathematical entity that gives the correct direction to the four-dimensional time.Taking into account the four-dimensional time as a vectorial quaternionic idea, we develop a set of generalizations and conclusions over the mechanics.In quantum mechanics, the four-dimensional time appears as an observable
Keywords Time as a quaternion  Mechanics in the four-dimensional time  Lagrangian with the four-dimensional time  Field in the four-dimensional time  Special relativity in the four-dimensional time  Time in quantum mechanics
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DOI 10.1007/s10701-010-9479-2
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